Diophantine Stability via Coherence Windows: A Study of Pell's Equation

This work introduces the notion of Coherence Windows in Diophantine stability theory, suggesting that certain ranges of discriminants DDD yield unusually small minimal solutions to Pell’s equation x2−Dy2=1x^2 - Dy^2 = 1x2−Dy2=1, while others yield chaotic large solutions. Computational analysis up to D=500D = 500D=500 supports this hypothesis. This structural lens could influence future models of solvability and complexity in Diophantine equations and algebraic number theory.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-04-26
DOI
https://doi.org/10.5281/zenodo.15285169
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

Diophantine Stability via Coherence Windows: A Study of Pell's Equation

Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
article

Diophantine Stability via Coherence Windows: A Study of Pell's Equation

article en

Abstract

This work introduces the notion of Coherence Windows in Diophantine stability theory, suggesting that certain ranges of discriminants DDD yield unusually small minimal solutions to Pell’s equation x2−Dy2=1x^2 - Dy^2 = 1x2−Dy2=1, while others yield chaotic large solutions. Computational analysis up to D=500D = 500D=500 supports this hypothesis. This structural lens could influence future models of solvability and complexity in Diophantine equations and algebraic number theory.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Openalex Percentile: Top 51%
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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Diophantine Stability via Coherence Windows: A Study of Pell's Equation · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS